Journal ArticleDOI

# Transverse anisotropy in the mixed-valent Mn2IIMn4IIIMn3IV single-molecule magnet

26 Feb 2008-Journal of Applied Physics (American Institute of Physics)-Vol. 103, Iss: 7

Abstract: High-frequency electron paramagnetic resonance measurements have been performed on a single-crystal sample of a recently discovered mixed valent Mn2IIMn4IIIMn3IV single-molecule magnet, with a spin S=17∕2 ground state. Frequency, temperature and field-orientation dependent studies confirm previously reported axial magnetic anisotropy parameters and also provide clear evidence for higher order (fourth and sixth) transverse terms that are responsible for the magnetic quantum tunneling observed in this system.
Topics: Magnetic anisotropy (57%), Single-molecule magnet (56%), Anisotropy (53%)

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Transverse anisotropy in the mixed-valent (Mn2Mn4Mn3IV)-Mn-II-
Mn-III single-molecule magnet
Citation for published version:
Datta, S, Milios, CJ, Brechin, E & Hill, S 2008, 'Transverse anisotropy in the mixed-valent (Mn2Mn4Mn3IV)-
Mn-II-Mn-III single-molecule magnet', Journal of applied physics, vol. 103, no. 7, 07B913, pp. -.
https://doi.org/10.1063/1.2838339
Digital Object Identifier (DOI):
10.1063/1.2838339
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Transverse anisotropy in the mixed-valent Mn2IIMn4IIIMn3IV single-
molecule magnet
Saiti Datta, Constantinos J. Milios, Euan Brechin, and Stephen Hill
Citation: J. Appl. Phys. 103, 07B913 (2008); doi: 10.1063/1.2838339
View online: http://dx.doi.org/10.1063/1.2838339
Additional information on J. Appl. Phys.
Journal Homepage: http://jap.aip.org/
Information for Authors: http://jap.aip.org/authors

Transverse anisotropy in the mixed-valent Mn
2
II
Mn
4
III
Mn
3
IV
single-molecule
magnet
Saiti Datta,
1,a
Constantinos J. Milios,
2
Euan Brechin,
2
and Stephen Hill
1
1
Department of Physics, University of Florida, Gainesville, Florida 32611, USA
2
School of Chemistry, University of Edinburgh, West Mains Road, Edinburgh, EH9 3JJ, United Kingdom
Presented on 9 November 2007; received 12 September 2007; accepted 29 November 2007;
published online 26 February 2008
High-frequency electron paramagnetic resonance measurements have been performed on a
single-crystal sample of a recently discovered mixed valent Mn
2
II
Mn
4
III
Mn
3
IV
single-molecule magnet,
with a spin S=17/ 2 ground state. Frequency, temperature and ﬁeld-orientation dependent studies
conﬁrm previously reported axial magnetic anisotropy parameters and also provide clear evidence
for higher order fourth and sixth transverse terms that are responsible for the magnetic quantum
tunneling observed in this system. © 2008 American Institute of Physics.
DOI: 10.1063/1.2838339
INTRODUCTION
Mixed-valent manganese clusters are considered ideal
candidates for single-molecule magnets SMMs as they of-
ten a exhibit large spin ground states and b possess Jahn–
Teller distorted Mn
3
III
ions which contribute to a large easy-
axis-type magnetic anisotropy.
1
These nanosized magnetic
materials display magnetization hysteresis and quantum tun-
neling of magnetization
2,3
QTM suggesting that they may
one day ﬁnd applications in information storage and possibly
quantum computation.
Here, we present single-crystal high-frequency electron
paramagnetic resonance HFEPR studies of a mixed valent
Mn
2
II
Mn
4
III
Mn
3
IV
complex hereafter Mn
9
Ref. 4兲兴, conﬁrming
the main ﬁndings of previous magnetic measurements and
inelastic neutron scattering INS studies, which showed that
Mn
9
has a spin ground state of S =17/ 2, a dominant axial
anisotropy parameterized by a D of value −0.24 cm
−1
, to-
gether with a fourth-order axial zero-ﬁeld splitting ZFS
term B
4
0
= +6.6810
−6
cm
−1
. Crucially, the present study
provides clear evidence for higher-order fourth and even
sixth order transverse anisotropy terms, which will clearly
inﬂuence the tunneling.
EXPERIMENTAL
The Mn
9
O
7
O
2
CCH
3
11
thme兲共py
3
H
2
O
2
complex
was prepared as reported previously.
4,5
Good sized black
crystals were obtained for single-crystal HFEPR measure-
ments. The metallic skeleton of the complex can be thought
to comprise two rings: a smaller Mn
3
IV
O
10+
triangle within a
Mn
4
III
Mn
2
II
O
6
4+
hexagon the charge is compensated by the
ligands. At ﬁrst sight, the magnetic core appears to have a
pseudothreefold topology. However, closer inspection of the
Mn valence states on the outer hexagon reveal a much lower
symmetry.
5
All of the Mn ions are in distorted octahedral
geometries with the Jahn–Teller elongation of the Mn
3+
ions
lying almost perpendicular to the plane of the
Mn
4
III
Mn
2
II
O
6
4+
hexagon. The complex crystallizes such that
there are two symmetry-equivalent, but differently oriented
molecules in the unit cell whose magnetic easy axes are ap-
proximately perpendicular to each other.
HFEPR experiments were performed on a single crystal
at various temperatures and frequencies from 50 to 200 GHz
with the dc magnetic ﬁeld applied along different crystallo-
graphic directions. The spectra were obtained at ﬁxed fre-
quencies and temperatures while varying the strength of the
dc magnetic ﬁeld. Details of the experimental technique can
be found elsewhere.
6,7
DATA AND DISCUSSION
Single-axis rotation studies were ﬁrst performed to
roughly determine the orientation of the crystal in the mag-
netic ﬁeld. Figure 1 shows temperature dependent spectra
obtained at 120 GHz, with the ﬁeld oriented reasonably close
30° to the easy axis associated with one of the two sites in
the unit cell. The intensities of the lowest ﬁeld peaks de-
crease upon increasing the temperature. This can be ex-
a
Electronic mail: saiti@uﬂ.edu.
FIG. 1. Color online Temperature dependent EPR spectra obtained at
120 GHz with the ﬁeld oriented reasonably close 30° to the easy axis of
one of the two molecular orientations. Each set of ﬁne structures is further
split into peaks labeled A and B, corresponding to inequivalent molecular
species with slightly different ZFS parameters D. See main text for expla-
nation of numbering.
JOURNAL OF APPLIED PHYSICS 103, 07B913 2008
0021-8979/2008/1037/07B913/3/23.00 © 2008 American Institute of Physics103, 07B913-1 Downloaded 09 Aug 2013 to 129.215.221.120. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions plained assuming a negative uniaxial anisotropy D 0. The appearance of two sets of peaks in Fig. 1 indicates that, in addition to the two different molecular orientations, there exist inequivalent Mn 9 species with slightly different ZFS parameters. We label the stronger peaks A and the weaker ones B. Peaks 1, 2, 3, 4, and 5 correspond to the following ﬁne-structure transitions: m S =− 17 2 15 2 ,− 15 2 13 2 ,− 13 2 11 2 ,− 11 2 9 2 , and 9 2 7 2 , respectively, where m S repre- sents the spin projection along the easy z axis of the crys- tal. Figures 2a and 2b display the positions of the ob- served EPR peaks plotted versus frequency for species A and B, and for the same ﬁeld orientation as the data displayed in Fig. 1. The solid curves were simulated using the following spin Hamiltonian Eq. 1, containing only axial ZFS pa- rameters H ˆ = DS ˆ z 2 + B 4 0 35S ˆ z 4 30SS +1兲其S ˆ z 2 + B B · g J · S ˆ . 1 The simulations assume S= 17 2 , and best overall agreement with the data is obtained with D=−0.24 cm −1 D = −0.25 cm −1 for species A species B, B 4 0 = +6.68 10 −6 cm −1 and g z =1.98. It is well documented that low- ﬁeld data especially extrapolations to B =0 obtained for ﬁelds close to the easy axis are insensitive to transverse an- isotropy terms. 8 As can be seen from Table I, the obtained axial parameters agree very well with previous magnetic and spectroscopic measurements. 4,5 Rotation about a single axis guarantees ﬁeld-alignment in the hard plane, although the orientation of the ﬁeld within the hard plane is not known. Detailed studies not shown allow identiﬁcation of one or other of the hard plane orien- tations from the angle dependence of the peak positions see Ref. 9. Figure 3a displays temperature dependent 52 GHz spectra for one of these hard-plane orientations. The A and B peaks are again observed, corresponding to the two species. The reversed ordering of A and B see Fig. 1 is consistent with Eq. 1. Peaks labeled A 1 ,A3 , and A5 likewise for the B peaks correspond to the following ﬁne-structure tran- sitions: m S =− 17 2 15 2 ,− 13 2 11 2 , and 9 2 7 2 , respectively, where m S now represents the spin projection along the high magnetic ﬁeld quantization axis. The low ﬁeld portion of the ﬁgure ﬁelds below A5 is complicated by absorptions due to the other molecular orientation. We now argue that fourth and higher-order transverse ZFS interactions are necessary in order to account for these spectra. It is well documented that HFEPR measurements FIG. 2. Frequency dependence of the peak positions associated with the two species: a Aandb B. Data were obtained at 5 K for the same ﬁeld orientation as in Fig. 1. The solid lines are simulations based on Eq. 1, using the parameters given in the main text. TABLE I. Comparison between ZFS parameters obtained from these studies EPR and the various magnetic measurements reported in Refs. 4 and 5. ZFS cm −1 FDMRS INS Magnetization -SQUID DFT EPR A EPR B D −0.2475 −0.2495 −0.293 −0.258 −0.235 −0.24 −0.25 B 4 0 / 10 −6 4.61 74 6.7 6.7 FIG. 3. Color online兲共a Temperature dependent EPR spectra obtained at 52 GHz with the ﬁeld in the hard plane of one of the molecular orientations. The ﬁne structure splitting A and B peaks can again be clearly seen refer to main text for explanation of numbering. At the highest temperature, additional peaks appear labeled X which we attribute to excited spin mul- tiplets. b Frequency dependence of the 7 K hard plane peak positions associated with species A the dashed curve corresponds to the data in a兲兴. The orientation of the ﬁeld within the hard plane is not known. The curves correspond to various simulations based on Eq. 1 with the inclusion of a rhombic term ES ˆ x 2 S ˆ y 2 兲兴. See main text for explanation. 07B913-2 Datta et al. J. Appl. Phys. 103, 07B913 2008 Downloaded 09 Aug 2013 to 129.215.221.120. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions with B c provide information concerning transverse terms. 8 In the following analysis, we constrain the axial terms D and B 4 0 on the basis of the simulations in Fig. 2. Density functional theory DFT calculations predict that Mn 9 pos- sesses a rhombohedral ZFS parameter E = 0.035 cm −1 . 5 We ﬁnd that it is impossible to obtain agreement between our results and simulations including only this interaction ES ˆ x 2 S ˆ y 2 兲兴, as demonstrated in Fig. 3b. The black curves were generated for two different E values and ﬁeld orientations relative to the hard axis within the hard plane: E =0.035 cm −1 , =25°; and E=0.015 cm −1 , =0° i.e., B x. These parameters were chosen in order to obtain agreement between the simulations and the A1 peak. However, as can be seen, agreement with A3 is not good. Conversely, the red curves were generated with the following parameters: E =0.035 cm −1 , =40° and E = 0.015 cm −1 , =38° i.e., B x. Here, the goal was to achieve agreement with the A3 peak. g x and g y were set to 2.00 for all of these simulations, as well as those in Fig. 4. The main result is that it is impossible to obtain anything approaching agreement with more than one of these peaks using only an E parameter. It turns out that, with the exception of A1 , all EPR peaks are reasonably close to the positions one would expect for extremely weak transverse second order anisotropy or =45°. In contrast, A1 is shifted considerably to higher ﬁelds. It is only possible to mimic its behavior using higher order transverse terms, as illustrated in Fig. 4. In fact, one can obtain good agreement with the hard-plane spectra for several different parameter sets. Examples are displayed in Fig. 4 involving purely B 4 2 O ˆ 4 2 a and B 6 6 O ˆ 6 6 b. The coefﬁ- cients are given in the captions. Interestingly, B 6 6 O ˆ 6 6 gives excellent agreement, whereas terms that one might expect to work well, such as B 4 3 O ˆ 4 3 , do not give good agreement. In reality, it is likely that the transverse Hamiltonian involves admixtures of all of these interactions, reﬂecting the pseudothreefold, 5 albeit low symmetry of the molecule. Only detailed multihigh-frequency measurements performed as a function of the ﬁeld orientation within the hard plane can resolve this issue, which would be greatly complicated by the multiple species, orientations, and the overall low sym- metry of this complex. Nevertheless, the present measure- ments serve a useful purpose, hinting at the signiﬁcant fourth and higher-order anisotropy that likely results as a conse- quence of S mixing brought about by low-lying excited spin states. 10 Indeed, the spectra in Fig. 3a clearly show features labeled X associated with the population of low-lying S 17 2 spin states. One ﬁnal point to note from Fig. 4a is the huge tunnel splitting of the lowest-lying m S = 17 2 doublet, which is clearly visible to the naked eye down to low ﬁelds. This suggests that a B 4 2 O ˆ 4 2 interaction would cause very fast tun- neling in this Mn 9 complex, which is not found experimen- tally and, therefore, seems to be unphysical. Again, this hints at the importance of multiple high-order transverse ZFS in- teractions that can account for both the EPR data presented here and the slow magnetization dynamics in the quantum regime. We also note that internal dipolar and hyperﬁne ﬁelds must be important for zero-ﬁeld QTM in these half integer SMMs. CONCLUSIONS Multi-high frequency and ﬁeld orientation dependent EPR studies have enabled a detailed characterization of the spin Hamiltonian of a mixed valent Mn 9 complex. These measurements hint at the importance of high- fourth and sixth order transverse anisotropy terms in the low tempera- ture quantum dynamics. ACKNOWLEDGMENTS This work was supported by the NSF DMR0239481 and DMR0506946. 1 D. N. Hendrickson, G. Christou, H. Ishimoto, J. Yoo, E. K. Brechin, A. Yamaguchi, E. M. Rumberger, S. M. J. Aubin, Z. Sun, and G. Aromi, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 376, 301 2002. 2 J. R. Friedman, M. P. Sarachik, J. Tejada, and R. Ziolo, Phys. Rev. Lett. 76, 3830 1996. 3 L. Thomas, F. Lionti, R. Ballou, D. Gatteschi, R. Sessoli, and B. Barbara, Nature London 383, 145 1996. 4 E. K. Brechin, M. Soler, J. Davidson, D. N. Hendrickson, S. Parsons, and G. Christou, Chem. Commun. Cambridge 19, 2252 2002. 5 S. Piligkos, G. Rajaraman, M. Soler, N. Kirchner, J. V. Slageren, R. Bircher, S. Parsons, H. U. Gudel, J. Kortus, W. Wernsdorfer, G. Christou, and E. K. Brechin, J. Am. Chem. Soc. 127, 5572 2005. 6 M. Mola, S. Hill, P. Goy, and M. Gross, Rev. Sci. Instrum. 71,1862000. 7 S. Takahashi and S. Hill, Rev. Sci. Instrum. 76, 023114 2005. 8 E. del Barco, A. D. Kent, S. Hill, J. M. North, N. S. Dalal, E. M. Rum- berger, D. N. Hendrickson, N. Chakov, and G. Christou, J. Low Temp. Phys. 140, 119–174 2005. 9 S.-C. Lee, T. C. Stamatatos, S. Hill, S. P. Perlepes, and G. Christou, Poly- hedron 26, 2225 2007. 10 A. Wilson, J. Lawrence, E.-C. Yang, M. Nakano, D. N. Hendrickson, and S. Hill, Phys. Rev. B 74, 140403 2006. FIG. 4. Color online Hard-plane data from Fig. 3 and simulations based on Eq. 1, with the additional inclusion of the higher-order transverse in- teractions a B 4 2 O ˆ 4 2 and b B 6 6 O ˆ 6 6 actual functions given in the ﬁgures. Both simulations agree reasonably well with the experimental data using the axial ZFS parameters determined from the simulations in Fig. 2, along with the following parameters: a B 4 2 =8.4 10 −5 cm −1 , b B 6 6 =8.4 10 −7 cm −1 , and =0 for both a and b. See main text for detailed explanation. The blue curves correspond to the splitting in the ground state m S = 17 2 doublet. 07B913-3 Datta et al. J. Appl. Phys. 103, 07B913 2008 Downloaded 09 Aug 2013 to 129.215.221.120. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions ##### Citations More filters Book ChapterDOI 01 Jan 2014- Abstract: This review covers single-molecule magnets, not only focussing on developments since 2005 but also including coverage of earlier work where necessary for understanding of recent results. The enormous growth of the area has led to an astonishing number of beautiful new molecules, and these structures are described. While work on 3d-single-molecule magnets has continued to create new materials for study, the major new path for exploration is studies of elements from other areas of the periodic table, particularly the 4f-elements. Here much higher energy barriers for magnetic relaxation are observed, and a much more varied chemistry is possible due to the high stability of the +3 oxidation state of the lanthanides. The chapter does not cover single ion magnets, which are reviewed elsewhere in this volume. 52 citations ##### References More filters Journal ArticleDOI Luc Thomas1, F. Lionti1, Rafik Ballou1, Dante Gatteschi2 +2 moreInstitutions (2) 12 Sep 1996-Nature Abstract: THE precise manner in which quantum-mechanical behaviour at the microscopic level underlies classical behaviour at the macroscopic level remains unclear, despite seventy years of theoretical investigation. Experimentally, the crossover between these regimes can be explored by looking for signatures of quantum-mechanical behaviour—such as tunneling—in macroscopic systems1. Magnetic systems (such as small grains, spin glasses and thin films) are often investigated in this way2–12 because transitions between different magnetic states can be closely monitored. But transitions between states can be induced by thermal fluctuations, as well as by tunnelling, and definitive identification of macroscopic tunnelling events in these complex systems is therefore difficult13. Here we report the results of low-temperature experiments on a single crystal composed of super-paramagnetic manganese clusters (Mn12-ac), which clearly demonstrate the existence of quantum-mechanical tunnelling of the bulk magnetization. In an applied magnetic field, the magnetization shows hysteresis loops with a distinct 'staircase' structure: the steps occur at values of the applied field where the energies of different collective spin states of the manganese clusters coincide. At these special values of the field, relaxation from one spin state to another is enhanced above the thermally activated rate by the action of resonant quantum-mechanical tunnelling. These observations corroborate the results of similar experiments performed recently on a system of oriented crystallites made from a powdered sample4. 1,522 citations Journal ArticleDOI TL;DR: It is proposed that these effects are manifestations of thermally assisted, field-tuned resonant tunneling between quantum spin states, and attribute the observation of quantum-mechanical phenomena on a macroscopic scale to tunneling in a large (Avogadro's) number of magnetically identical molecules. Abstract: We report the observation of steps at regular intervals of magnetic field in the hysteresis loop of a macroscopic sample of oriented M{\mathrm{n}}_{12}{\mathrm{O}}_{12}$(C${\mathrm{H}}_{3}$COO${)}_{16}$(${\mathrm{H}}_{2}$O${)}_{4}\$ crystals. The magnetic relaxation rate increases substantially when the field is tuned to a step. We propose that these effects are manifestations of thermally assisted, field-tuned resonant tunneling between quantum spin states, and attribute the observation of quantum-mechanical phenomena on a macroscopic scale to tunneling in a large (Avogadro's) number of magnetically identical molecules.

1,333 citations

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Abstract: The symmetry of magnetic quantum tunneling (MQT) in the single molecule magnet Mn2-acetate has been determined by sensitive low-temperature magnetic measurements in the pure quantum tunneling regime and high frequency EPR spectroscopy in the presence of large transverse magnetic fields. The combined data set definitely establishes the transverse anisotropy terms responsible for the low temperature quantum dynamics. MQT is due to a disorder induced locally varying quadratic transverse anisotropy associated with rhombic distortions in the molecular environment (2nd order in the spin-operators). This is superimposed on a 4th order transverse magnetic anisotropy consistent with the global (average) S4 molecule site symmetry. These forms of the transverse anisotropy are incommensurate, leading to a complex interplay between local and global symmetries, the consequences of which are analyzed in detail. The resulting model explains: (1) the observation of a twofold symmetry of MQT as a function of the angle of the transverse magnetic field when a subset of molecules in a single crystal are studied; (2) the non-monotonic dependence of the tunneling probability on the magnitude of the transverse magnetic field, which is ascribed to an interference (Berry phase)effect; and (3) the angular dependence of EPR absorption peaks, including the fine structure in the peaks, among many other phenomena. This work also establishes the magnitude of the 2nd and 4th order transverse anisotropy terms for Mn12-acetate single crystals and the angle between the hard magnetic anisotropy axes of these terms. EPR as a function of the angle of the field with respect to the easy axes (close to the hard-medium plane) confirms that there are discrete tilts of the molecular magnetic easy axis from the global (average) easy axis of a crystal, also associated with solvent disorder. The latter observation provides a very plausible explanation for the lack of MQT selection rules, which has been a puzzle for many years.

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